A telecommunication system may include a transmitter for encoding information to be transmitted as an electromagnetic wave, a transmission medium which provides a conduit for the transmission of the electromagnetic wave and a receiver for receiving and processing the information bearing electromagnetic wave. A telecommunication system may utilize a waveguide as a transmission medium. A waveguide is a structure that guides or constrains the propagation of electromagnetic radiation. A waveguide may comprise a system of material boundaries in the form of a solid dielectric. In telecommunications, optical fibers are often utilized as waveguides.
It is desirable to increase the bandwidth or transmission rate of a telecommunication system for several reasons. First, greater bandwidth is required to support modern telecommunication applications such as that employed in data centers, or for live video and audio, multimedia and other bandwidth intensive applications. In addition, for efficiency and cost reasons it is desirable to increase the bandwidth of telecommunication systems. Therefore, it is important to address the physical limitations of waveguides for transmitting high bandwidth electromagnetic signals.
Dispersion is a significant physical phenomenon limiting the ability to successfully transmit and recover an information bearing electromagnetic wave over a communication channel. The phase velocity of any spectral component within a transmission medium will depend upon the index of refraction for the physical medium. Typically, the index of refraction of a transmission medium will be frequency dependent. Waveguide dispersion occurs when the speed of a wave in a waveguide such as optical fiber depends upon its frequency. The transverse modes for waves confined with a waveguide generally have different speeds depending upon the frequency. A similar phenomenon is modal dispersion caused by a waveguide having multiple modes at a given frequency, each of which propagates at a different speed.
Waveguide dispersion leads to signal degradation in telecommunication systems because the varying delay in arrival time between different components of a signal effectively degrades the pulse characteristic of pulses transmitted through the waveguide. This phenomenon is often referred to as intersymbol interference (“ISI”). Adjacent symbols represented as pulses effectively “run into” one another, and energy may exist at a particular sample instant of one symbol that actually includes energy associated with an adjacent symbol
Thus, it is necessary to correct for error sources such as dispersion and associated ISI that may be introduced in a received signal transmitted over a communication channel. Typically, a receiver will be equipped with a signal processing system to correct for dispersion effects introduced by the communication channel. These signal processing systems often analyze statistical properties of the communication channel in order to cancel the ISI. The signal processing system typically utilizes one or more equalizers to perform these corrections. One type of equalizer often used is a feed forward equalizer (“FFE”), which attempts to correct for pre-cursor ISI (in which a current symbol is affected by a following symbol). Often an FFE may be combined with a decision feedback equalizer (“DFE”), which attempts to correct for post-cursor ISI (in which a current symbol is affected by a preceding symbol).
There are a number of technical challenges that may arise in building signal processing systems to correct for dispersion and ISI, which become particularly acute in communication systems employing a high baud rate or symbol rate. First, it is desirable to perform signal processing operations in the digital domain as it is often easier to achieve a higher SNR than an equivalent analog system. Second, digital systems offer the advantage of significantly lower complexity in signal layout and design and the opportunity to easily modify the signal processing routines employed.
A digital signal processing system necessitates a conversion of a received analog signal into a digital format. In general, it may be difficult and expensive to build a serial ADC to operate at baud rates in excess of 1.5-2 GHz. This is problematic because it is often desirable to build communication systems that operate around the order of at least 10 GHz. Similar issues exist for designing and building equalizers that may operate at high data rates.
A second technical issue relates to the time varying nature of communication channels, which impacts the performance of timing recovery operations at a receiver. A transmitter will typically include a clock, which is used to encode a data signal onto a carrier signal for transmission over the channel. The transmitter clock will determine the rate at which symbols are provided over the communication channel.
The receiver will typically also require a clock, which ideally should be phase locked to the transmitter clock in order to accurately recover the symbols transmitted by the transmitter over the communication channel. However, the transmitter and receiver clocks typically will experience a drift with respect to one another resulting in a frequency offset between the two. The phase being the integral of the frequency, will therefore suffer an offset between the transmitter and receiver clocks. Thus, receivers in communication systems typically include a timing recovery circuit to attempt to synchronize the transmitter clock with the receiver clock.
Digital communication systems may employ a method referred to as baud rate or symbol rate sampling, in which the received signal is sampled at the baud rate. Because the entire analog signal need not be recovered in a communication system, it is not necessary to sample at the Nyquist rate. However, baud rate sampling imposes significant constraints on the accuracy of the timing recovery operations performed at the receiver in order that the receiver samples a valid and stable signal.
As noted above, communication systems require a physical medium for the transmission of communication signals. The nature of the physical medium underlying the communication system may often be time varying. Typically this time dependence will be on a time scale relatively long compared with the baud rate. In the case where the communication channel may be approximated by its first order behavior, higher order effects are small, the channel characteristic is time invariant and initial conditions are known, the effect of the channel on a transmitted signal may be characterized by a impulse response or Green's function, which describes the response of the channel to an impulse signal. In conventional timing recovery systems utilizing conventional algorithms, the time varying nature of the channel characteristic may not be accounted for, reducing the ability of the signal processing system to perform accurate baud rate sampling and thereby effectively cancel the undesirable ISI effects.